Economic Versus Political Symmetry and the
Welfare Concern with Market Integration and Tax
Competition
Anke S. Kessler, Christoph Lülfesmann, and Gordon M. Myers∗
Final Version: July 2001
forthcoming in Journal of Public Economics
Abstract
The paper studies the implications of increased capital market integration
and the associated increased tax competition for world welfare. We consider a
population with heterogenous endowments of capital in a model of redistributive
politics. We show that if countries have the same average capital endowments
but differ with respect to the endowments of their decisive majority, autarky
may be socially preferred to integration under any aversion to inequality. We
then reverse the conclusion by assuming that the decisive majority has the same
endowment but countries differ in their average capital endowments. In proving
these results we show that integration may decrease world output and increase
the utility of the poorest members of the economy.
JEL Classification: D78, H23, H77
1
Introduction
Surely, a key feature of the world economy in the twentieth century has been increased
economic integration of international markets. The mobility of factors and goods has
been enhanced as new technologies have dramatically reduced transportation and communication costs and as institutional or political barriers to that mobility have fallen.
It is then not surprising that one of the important themes in the media and the economics literature is about the consequences of a globalized economy on the economic
structure of our societies.
∗
University of Bonn, Department of Economics, Adenauerallee 24–42, 53113 Bonn, Germany for
the first two authors, and Simon Fraser University, Department of Economics, 8888 University Drive,
Burnaby BC, V5A 1S6, Canada for the last author. We are grateful to two anonymous referees and
the Editor for valuable comments on an earlier version. Financial support by SSHRC and the German
Academic Exchange Service is gratefully acknowledged. Remaining errors are our own.
1
For most economists integration of international markets is viewed as a desirable
development. At its core, it is about individuals exploiting mutually beneficial gains
from trade with the obvious potential for the enhancement of efficiency. But increased
integration also implies increasingly mobile tax bases, and as pointed out by Edwards
and Keen (1996), this in turn raises the prospect of increasingly fierce international tax
competition as national authorities attempt to expand their tax base by offering more
favourable tax treatment. It has been argued that as tax rates are reduced to avoid
flight of the tax base, the ability of national governments to provide public services
and to undertake redistribution at traditional levels is threatened.
The competition for mobile capital is considered by some authors as one of the
greatest dangers to the survival of the welfare state. Sinn (1994), for example, predicts
an European Union where “...fiscal competition will wipe out redistributive taxes on
mobile factors and reduce the tax system to mere benefit taxation”.1 He argues that
the losers will include immobile workers who will bear a larger share of taxation and
the poor who will lose because governments will not be able to maintain their current
scales of redistribution.
The theoretical literature on capital tax competition is voluminous and began with
the ideas of Hamada (1966) and Oates (1972), and the works of Wilson (1986), Zodrow
and Mieszkowski (1986), and Wildasin (1988). This research largely supports the
view that capital tax competition may lead to inefficiencies and reduce redistribution.
The logic is simple. Imagine countries non-cooperatively choosing taxes on freelymobile locally-employed capital to finance a uniform public service. As discussed in
Wildasin (1988), when a government of one country considers increasing its tax rate in
accounting for the capital flight it does not consider the benefit of increased tax base
in the competing countries (a beneficial externality). Thus each country chooses a tax
in equilibrium such that Pareto improvements are possible by a coordinated increase
in tax rates and benefit levels.2
We consider a positive model of redistribution in the presence of fiscal competition. Capital and domestic labour are combined to produce a composite good. In each
country, the redistributive policy consists of a tax on locally employed capital and a
1
For antidotal evidence of tax competition, see Edwards and Keen (1996). The concern amongst
policy practitioners that capital market integration intensifies tax competition is also evident in the
policy coordination guidelines recently issued by the OECD and the EU [see OECD (1998) and
European Commission (1998)].
2
We refer the reader to a recent survey by Wilson (1999) which provides many references.
2
uniform benefit for redistribution and is democratically chosen by its self-interested
inhabitants. By assumption, a country’s decisive majority is endowed with less than
the country’s per capita capital stock which is well in line with empirical evidence.
The model is designed to lead to stark redistributive politics which captures the redistributive concern above, to the extreme. Specifically, in the absence of integration (i.e.,
autarky) the equilibrium will involve expropriative capital taxation, full redistribution,
and complete equality within a country. From this simple benchmark we study the
integration of capital markets and determine equilibrium tax policies and the implied
allocation in the capital tax competition game. On the distributional side the taxation of capital normally declines due to the voters’ worry about capital flight. As a
consequence, the equilibrium is characterized by fiscal competition in the sense that
a (capital poor) majority in each country could be made better off by a coordinated
increase in capital taxes. The logic is exactly the bidirectional beneficial externality
discussed above.
Yet, in our opinion, the question which is not fully addressed in the existing literature is whether we should therefore be concerned about this “collapse” of the welfare
state. This short paper focuses on this question. One might imagine that an answer
would depend on the theory of justice — if the primary criteria is wealth maximization
then integration may be desirable and if the primary criteria is helping the poor then
integration may be undesirable. But this need not be the case. On one hand, we show
that if countries are symmetric in their per capita endowments of capital but differ
in the capital endowment of their decisive majority then autarky is socially preferred
to integration under any world welfare function, in particular, the result holds for any
aversion to inequality. On the other hand, we show that if countries are asymmetric in their per capita endowment of capital and symmetric in the capital endowment
of their decisive majority then integration can be socially preferred to autarky under
any aversion to inequality. In the process we also demonstrate that with a political
equilibrium model of tax competition integration can reduce world output (which is
necessary for autarky to dominate integration at a zero aversion to inequality) and
can help the poorest individuals in the economy (which is necessary for integration to
dominate under an infinite aversion to inequality).
The remainder of the paper is organized as follows. Section 2 lays out the model
and characterizes equilibrium outcomes under autarky (Subsection 2.1) and integration
(Subsection 2.2.), respectively. The welfare comparison is considered in Section 3. We
3
briefly discuss the results and possible extensions of the model in a concluding Section
4.
2
The Model
Consider an economy that consists of two countries j = 1, 2, inhabited by a continuum
of individuals who derive income from their factor endowments. While everybody
inelastically supplies one unit of labour, individuals differ in their endowment k i of
capital. For simplicity, we assume that there are only two groups i ∈ {P, R} of capital
owners in each country with kjP < kjR .3 In autarky capital can only be invested at
home while with market integration it can costlessly be invested wherever the after–tax
return is highest. Alternatively, capital owners may decide not to invest their capital
at all (free disposal) if they incur losses. For simplicity, we assume that individuals
are immobile and that the population (labour supply) is the same in both countries.
Labour and capital are used as inputs in the production of the composite and numeraire
commodity c by competitive firms. Both countries have access to a constant returns
to scale production function which written in per-capita terms is yj = f (kj ) where yj
and kj denote per capita output and per capita capital employed in j, respectively. We
further assume that f 0 (kj ) > 0, f 00 (kj ) < 0, f 000 (kj ) ≥ 0.4 The first–order conditions
for profit maximizing imply that factors are paid the marginal product for capital
rj (kj ) ≡ f 0 (kj ) and using the zero profit condition the wage, wj (kj ) = f (kj ) − rj (kj )kj .
A country’s policy (tj , gj ) consists of a source–based tax tj on each unit of capital
employed in j and a uniform per–capita grant gj that redistributes public revenues
among the residents of j. Accordingly the public budget constraint expressed in per–
capita terms is
g j ≤ tj kj .
(1)
Policies are determined by majority vote of the inhabitants of country j. The timing
is as follows: in the first stage, the inhabitants of each country j simultaneously vote
on a tax rate tj . In the second stage, individuals simultaneously decide whether and, if
investment abroad is feasible, where to invest their capital. Finally firms hire factors
3
Extending the model to continuous distributions of capital is straightforward. We will discuss this
in our concluding section.
4
The assumption on the third derivative of f (.) is necessary to ensure the equilibrium existence
in the fiscal-competition game [see Laussel and Le Breton (1998)]. It is satisfied by all specifications
frequently used in the literature such as Cobb-Douglas, quadratic or exponential production functions.
4
and produce, residents receive their factor incomes, pay taxes, collect social benefits,
and consume. An equilibrium must therefore satisfy the following conditions: a) given
the tax policy in the other country, the implemented tax policy is preferred to any
other by a majority in each country (political equilibrium); b) investment decisions are
optimal given tax rates (t1 , t2 ) and c) markets clear.
Using the fact that (1) will be always be binding, we can rewrite the consumption
(income) of a country j citizen who belongs to group i and has invested at home as
cij = wj (kj ) + [rj (kj ) − tj ]kji + tj kj
= f (kj ) − [rj (kj ) − tj ][kj − kji ]
(2)
where the last equality follows from wj (kj ) = f (kj ) − rj (kj )kj . To facilitate our subsequent welfare analysis, we assume that (2) also measures the utility of the respective
individual.
Let k¯j be the per–capita endowment of capital and kjm be the capital endowment
of the group that is in a majority in country j. The economy-wide average capital
endowment is denoted by k̄. In the remainder, we assume that the (capital) poor are
in a majority in both countries and that their endowment falls short of the average
capital stock in the economy:
Assumption: kjm = kjP and kjm < k̄,
kjm
j ∈ {1, 2}
This assumption is well in line with empirical evidence. As the first part implies
< k¯j , it ensures that redistributive taxation will be supported by the (capital-poor)
majority both within each country and for the economy as a whole. The political
equilibrium now simply involves maximizing (2) for the majority group i = P , j = 1, 2.5
2.1
Autarky
Under autarky all individuals must invest at home so that kj = k̄j . The most preferred
tax rate of the majority in country j is the solution to
max f (k¯j ) − [rj (k¯j ) − tj ][k¯j − kjm ],
tj
5
Note that (2) continues to hold if a group i individual has invested his capital abroad because net
returns to capital rj − tj have to be equalized in equilibrium.
5
subject to the constraint that the after-tax return to capital, ρj = rj (k¯j ) − tj , is nonnegative.6 Because the objective function is monotonically increasing in tj , the political
equilibrium under autarky involves expropriative taxation of capital or
¯
tA
j = rj (kj )
and
¯
ciA
j = f (kj )
(3)
for all i ∈ {P, R} and j ∈ {1, 2}. Although this outcome under autarky is extreme it
will serve as a useful benchmark for welfare comparisons to integration. Because it is
characterized by complete redistribution within a country it will allow us to capture the
concern about the breakdown of the welfare system under integration and the ensuing
capital tax competition in full.7
2.2
Integration
Now suppose that individuals can freely and costlessly invest their capital in either
country. Since capital is perfectly mobile, its net return must be equal across countries
in an equilibrium at the investment stage or
ρ = r1 (k1 ) − t1 = r2 (k2 ) − t2 .
(4)
As long as all capital is employed, i.e., [k1 +k2 ]/2 = k̄ where k̄ is the economy wide average capital stock, (4) uniquely determines the capital stock in each country, kj (t1 , t2 ),
and the equilibrium net return, ρ(t1 , t2 ), as a function of the tax rates.8 Implicitly
differentiating (4) yields the investment responses for ρ ≥ 0
∂kj (t1 , t2 )
1
= 00
< 0.
∂tj
[f (k1 ) + f 00 (k2 )]
(5)
6
This constraint follows from our assumption of free disposability. Note that if ρj = rj (k¯j )−tj < 0,
capital owners would withdraw their capital from the market until ρj = rj (kj ) − tj = 0 holds again.
Due to kj < k¯j , the consumption (2) of all individuals would be cij = f (kj ) < f (k¯j ). Since a tax rate
tj = rj (k¯j ) would be unanimously preferred, such a situation cannot be an equilibrium.
7
The simplifying abstraction which leads to expropriative taxation is the assumption that capital
is a fixed endowment and the resulting lump–sum nature of taxation in autarky. Due to the distortion
of savings decisions and other costs of government taxation the marginal costs of public funds may
exceed unity [see Persson and Tabellini (1992) and Perotti (1993) for formalizations along this line].
The numerical examples in Appendix 2 allow for a specific cost to taxation so that taxes are not
expropriative and show that our qualitative results continue to hold.
8
A formal argument why there can be no equilibrium where [k1 + k2 ]/2 < k̄ (the capital stock is
not fully utilized) can be found in Appendix 1.
6
Accordingly,
f 00 (kh )
∂rj (t1 , t2 )
∂ρ(t1 , t2 )
= − 00
=
− 1 ∈ (−1, 0).
00
∂tj
f (k1 ) + f (k2 )
∂tj
(6)
The equilibrium tax rate in country j is now determined by
max f (kj (t1 , t2 )) − ρ(t1 , t2 )[kj (t1 , t2 ) − kjm ],
tj
th given, j 6= h, j, h ∈ {1, 2}
(7)
subject to (4), [k1 + k2 ]/2 = k̄ and ρ(t1 , t2 ) ≥ 0. Using (5) and (6), the first–order
conditions can be written as
tj = −f 00 (kh (t1 , t2 ))[kj (t1 , t2 ) − kjm ],
j 6= h, j, h ∈ {1, 2}.
(8)
Under our assumptions, equation (8) implicitly defines a single valued and increasing
br
best–response function tbr
j (th ) which is valid for ρ(tj (th ), th ) ≥ 0. Otherwise, the
0
solution to (7) is uniquely given by tbr
j (th ) = rj (t1, t2 ) = f (kj (t1 , t2 )), where kj is
derived according to (4) with [k1 + k2 ]/2 = k̄.9
In both cases, tbr
j (th ) is the unique best reply of the electorate in country j to the
policy th chosen by the electorate in the other country. The equilibrium tax rates
(t∗1 , t∗2 ) can be found at a point where the reaction functions intersect. Once those are
determined, all other variables are determined and will be denoted by superscript ∗ in
what follows.
3
Welfare Comparison
3.1
Economic Symmetry and Political Asymmetry
For some economists it would be taken as obvious that there are efficiency benefits to
integration of world capital markets. After all integration simply allows individuals to
exploit gains from trade.
Proposition 1. Suppose countries have the same per-capita capital stock but differ in
the capital endowment of the decisive majority. Then, there exists a unique equilibrium
under integration, which is characterized by t∗1 6= t∗2 . Hence, autarky is socially preferred
to integration under any individualistic world welfare function satisfying anonymity.
9
Note that in this case, t∗j (th ) is decreasing in th . A derivation of the best reply functions and their
properties is provided in Appendix 1.
7
Proof. The maximization of world output requires r1 (k1 ) = r2 (k2 ) or identical
capital to labour ratios, k1 = k2 = k̄. Now consider k¯j = k̄ for all j and without loss of
generality k1m > k2m . Autarky maximizes world output and leads to complete equality,
that is, an equalitarian allocation, see (3). The equilibrium with integration does not
a) maximize world output or b) lead to complete equality:10
a) Assume that the equilibrium with integration did maximize output, i.e., k1 =
k2 = k̄. Then r1 (k1 ) = r2 (k2 ) implies t∗1 = t∗2 by (4). In the appendix, we show that for
k1m > k2m , there can be no equilibrium where ρ∗ = 0 and k1 = k2 = k̄ . If ρ∗ > 0, k1 =
k2 = k̄ implies k1m = k2m from(8)—a contradiction to k1m > k2m .
b) Under our assumption k¯j > kjm , there is inequality within a country for ρ∗ > 0 .
Given k1∗ 6= k2∗ , if ρ∗ = 0 there is inequality across countries as f (k1∗ ) 6= f (k2∗ ).
The equilibrium utility profile under autarky is along the equal utility line and characterized by a higher total utility than under integration. Autarky is therefore socially
preferred under any individualistic world welfare function satisfying anonymity.11 ¥
The logic of the result is simple: there is no efficiency or distributional benefit of
integration when k¯j = k̄ for all j. Conversely, there is an efficiency loss as the different
political objectives of the majority will distort the allocation of capital with unequal
capital taxes [see (8)] and a distributional cost through the reduced control of capital
taxes by the voters due to their accounting for capital flight.
On first thought, a primary benefit of integration would seem to lie in increased
world output. If output increases as a consequence of integration, it must be socially
preferred with a sufficiently low aversion to inequality. That opening borders to capital
flows can actually reduce world output may seem unusual because the result requires
that capital flows in the wrong direction from an efficiency perspective. Thus, even
given the finding above, one might wonder about its robustness. It turns out that the
result is only unusual from the perspective of the type of model frequently used in
the existing capital tax competition literature. Consider a homogeneous population
within each country and governments that are benevolent (maximize national income).
A useful feature of our model is that it contains that model as a special case: let
kji = k̄j for all i ∈ {P, R}, i.e., the population is homogeneous within each country.
The objective in (2) is then proportional to national income. In this case capital
will not move in the wrong direction with integration, that is, if country 1 is capital
10
11
For a complete proof of existence and uniqueness, see Appendix 1.
The role of anonymity is discussed below.
8
abundant or k̄1 > k̄2 then country 1 will not import capital or k1∗ ≤ k¯1 . To see this,
suppose k1∗ > k̄1 . Then using [k1 + k2 ]/2 = k̄ = [k̄1 + k̄2 ]/2, we have k2∗ < k̄2 and
r1 (k1∗ ) < r2 (k2∗ ). The latter implies t∗1 − t∗2 < 0 by (4), which is inconsistent with
equilibrium because from (8) with kjm = k̄j , the exporter subsidizes capital (t2 < 0)
and the importer taxes capital (t1 > 0) in the attempt at manipulating the terms of
trade, ρ. But once the model is generalized to allow for a heterogeneous population
with redistributive and democratically chosen policies, that is no longer true. What is
important for the political equilibrium is the factor endowment of a country’s decisive
majority (its median voter), not its mean endowment.
In Appendix 2 we offer an example where k̄1 6= k̄2 and k1P 6= k2P (countries and decisive majorities are asymmetric). The example specifies a Cobb–Douglas production
function and also considers costs of taxation so that taxes in autarky are not expropriative. Still, integration reduces output because capital flows in the wrong direction
and autarky is socially preferred to integration under any aversion to inequality.
3.2
Economic Asymmetry and Political Symmetry
For other economists it would be taken as obvious that there are distributional costs
associated with the integration of world capital markets. After all the potential for
capital flight leads to an incentive to cut capital taxes and levels of redistribution.
Define
b
k ≡ k̄ + f 0 (k̄)/f 00 (k̄) < k̄.
Proposition 2. Suppose countries differ with respect to their per-capita capital endowments but are symmetric in the endowment of the decisive majority. If k m ≥ b
k,
k1∗
k2∗
j
t∗1
the unique equilibrium under integration is characterized by
=
= k̄ and = t∗2 ,
and involves ρ∗ → 0 as kjm → b
k. If kjm < b
k, we have ρ∗ = 0 and there is always an
equilibrium with k1∗ = k2∗ = k̄. Therefore, there exists a critical value k max ∈ (b
k, k̄)
with ρ∗ > 0 such that if the majority in each country has less capital than k max , integration is socially preferred to autarky under any individualistic world welfare function
satisfying anonymity.
Proof: Suppose k1m = k2m so that the reaction functions are symmetric. If ρ∗ > 0,
they cross only once and the first-order conditions (8) must hold for both countries at
t∗1 = t∗2 = t∗ and k1∗ = k2∗ = k̄. Hence,
t∗ = −f 00 (k̄)[k̄ − kjm ] < r∗ = f 0 (k̄)
9
⇔
kjm > b
k.
If kjm = b
k, there is again a unique intersection where both countries set a common
tax rate t∗ = r∗ (k̄). Finally, if kjm < k̂, the reaction functions no longer intersect over
the range where both are positively sloped. Then, there is a continuum of equilibria,
including the symmetric equilibrium where t∗j = t∗ = r∗ (k̄) holds (see Appendix 1 for
details).
Under autarky there is inequality between countries and world output is not maximized. For symmetric endowments of the majority in each country kjm ≤ b
k, there
always exists a symmetric equilibrium under integration in which the utility profile is
along the equal utility line and characterized by a higher total utility than under autarky. Integration is then strictly preferred to autarky under any individualistic world
welfare function satisfying anonymity. By continuity, then, this must still be true for
capital endowments k m larger than, but close to, b
k (implying ρ∗ > 0) and the result
j
follows.¥
The logic of the result is that there are potential efficiency benefits of integration
when k¯1 6= k¯2 and there is no inefficiency loss as symmetric median voters do not distort
the allocation of capital with unequal capital taxes. Further, if the capital endowment
of the poor majority is sufficiently small (the political will to redistribute sufficiently
large), integration and the associated fiscal competition effect does not give rise to
distributional costs. This latter point requires some explanation. Even though there is
loss of control over capital taxes by the decisive voters with integration, in particular,
the conventional logic of capital taxes being too low from the perspective of a majority
is correct, we may still approach expropriative taxation in the unique equilibrium. This
happens if the redistributive incentive of the capital poor majority is very pronounced,
i.e., if kjm approaches the lower bound b
k.12 If kjm falls below b
k, the incentive is so strong
that the upper bound on taxes (due to free disposability) becomes binding and we
always have 100% taxation. This is obviously a stark conclusion that may not survive
in more general models. But as stated in the Proposition, expropriative taxation is
k, we have ρ∗ > 0. Nevertheless,
not required: for values k m larger than (but close to) b
j
integration is socially preferred to autarky even when society is very concerned with
inequality. The reason is that besides the efficiency effects and the loss of redistributive
Note, however, that b
k as defined above need not be positive for all conceivable production functions
and parameter values, i.e., the full-taxation equilibrium does not always exist. In the case of a CEStechnology, for instance, it is easily verified that b
k ≥ 0 only if the elasticity of substitution is sufficiently
low.
12
10
power for the poor with integration there is a third effect which can make integration
beneficial from a distributional point of view. Consider an infinite aversion to inequality
(Rawlsian) and the fact that the poorest individuals in the economy (the poor in
the poor country) can be helped by integration due the inflow of capital and the
correspondingly higher wages.
In Appendix 2 we provide an example where k1m 6= k2m and k1P 6= k2P (countries and
majorities differ). The parameter values are such that k P > b
k so ρ∗ > 0 and integration
j
is socially preferred to autarky for any aversion to inequality. In the example, the
relatively rich country has a relatively wealthy (poor) majority and exports capital
with integration. It can be shown (see below) that the majority in the rich country
must be worse off with integration, it sees its wages drop and loses some control over
redistribution. Nevertheless the result is consistent with Proposition 2 – no matter
your aversion to inequality integration is socially preferred to autarky. But notice if
you were nationalist (of the rich country) and your ethics involved a significant degree
of aversion to inequality you could conclude that integration was not a good policy.
The reason why our result still holds is that the poorest individuals in the economy
(the poor in the poorer country) are better off under integration and because of the
anonymity axiom we employ. This most basic social choice axiom rules out greater
social weight on an individual based on ethically arbitrary accidents of birth such as
sex and race. In ruling out racism and sexism as ethically untenable principles, it also
rules out place of birth, that is, nationalism as ethically untenable.13
4
Conclusion, Discussion, and Extensions
While integration of markets is about individuals exploiting gains from trade it is
also about the political determination of the barriers to that trade. So besides the
obvious potential for efficiency enhancing integration there is also the possibility that
integration can hinder efficiency. Further, besides the potential for a race to the bottom
and its impact on inequality in our societies, integration may increase the well–being of
the poorest in the poor countries by increasing the amount of capital with which they
work. Thus there are simple trade–offs on both efficiency and distributional grounds
in considering the consequences of increased integration for welfare.
This paper has studied the implications of these trade–offs. We have considered
13
Of course, this does not say that nationalism will not affect feasibility and, hence, social choices.
11
two countries with heterogeneous populations which pursue democratically chosen redistributive policies. How world welfare was affected by integration was shown to
depend on how much the countries differ with respect to their economic and political conditions. In particular, if they share the same per-capita factor endowments,
but differ with respect to the endowments of their decisive majority, autarky may be
socially preferred to integration under any aversion to inequality. Conversely, if the
decisive majority has the same endowment but countries differ in their average capital
endowments, integration may be socially preferred to autarky under any aversion to
inequality.
The framework in which our results were derived could be extended in several directions. First, the assumption that there are only two groups of capital owners in each
country can easily be relaxed. Indeed, because the only country-specific parameters
of the distribution that matter for the analysis are average and median endowments,
our results immediately carry over to more general (non-degenerate) distributions. To
see this, note that given the specific structure of individuals’ preferences, the voter
with median capital endowment kjm in each country will be decisive.14 If we continue
to realistically assume kjm < k̄j and kjm < k̄ for j ∈ {1, 2}, equilibrium policies are
still characterized by (3) and (8), and the properties of the respective equilibria are
unchanged. Moreover, an equilibrium that involves complete equality and maximal
world output can still be used as a suitable reference point for the welfare analysis.
Hence, both Propositions 1 and 2 fully apply.
Second, we have assumed that countries conduct purely redistributive politics,
which allowed us to focus on the redistributive concern with globalization. A natural extension would be to consider more general public good provision.15 Suppose
we add a separate, publicly supplied good Gj with M RT = 1 and U (cij , Gj ) where
cij = wj + [rj − tj ][kj − kji ] + gj and Gj = tj kj − gj , then along with the redistributive
incentive to use capital taxes there would be an incentive to get the right mix of public
and private expenditure. The latter objective could be achieved by using gj as uniform
head subsidy (tax), which leaves the majority free to use the capital tax for purely
14
Since the utility function (2) is linear in the parameter k i , it belongs to the class of intermediate
preferences as defined by Grandmont (1987). For this type of preferences, the majority rule preference
relation coincides with the preference relation of the median voter [for a formal proof in the present
context, see Kessler et al. (1998)]. The analysis in the Appendix then continues to apply.
15
Note that per-capita transfers gj are an extreme case of a publicly provided good that is a perfect
substitute for the private good.
12
redistributive reasons. If, on the other hand, the transfer gj is no longer available when
Gj is provided then there would be two targets (redistribution and the public/private
mix) but only one tax instrument, the capital tax tj . In this case the stark nature of
our results would clearly be mitigated. In particular, taxation would not necessarily
be expropriative under autarky because that would normally imply too much public
good. Similarly, there would be a reduced incentive to cut capital taxes in response to
integration and fiscal competition because that could imply too little public good.
Third, countries were assumed to be symmetric in their labour endowments. Although differences in labour endowments are of no consequence for Proposition 1, they
will matter for the result in Propostion 2 for the following reason. In a traditional
model of capital tax competition (with homogeneous population within countries and
a public good) Bucovetsky (1991) and Wilson (1991) show that the smaller country, in
terms of labour endowment, sets a lower equilibrium tax rate than the larger country.
In this case, the small country could even win the tax competition “war” in the sense
that it could be better off at the inefficient non-cooperative equilibrium than at the
free trade allocation (with equal marginal products of capital and Samuelson conditions). Translated to our framework, these findings suggest that if countries differ in
their labour force, the welfare consequences of integration are ambiguous even if other
determinants of the electorate’s political will (the capital endowment of the decisive
majority) are equal. Specifically, integration may now be detrimental to world output
and to the poor majority in the larger country, which highlights the importance of
sufficiently similar political conditions across countries for integration to be beneficial
from a normative point of view. A full-fledged analysis of this generalization is beyond
the scope of the present paper, however.
Our analysis has attempted to provide some new insight or perspective on the ongoing normative globalization debate. But the related positive question is also of interest.
Under which conditions could we expect a majority in each country to favour capital
market integration? One way to address this issue in the present model could be to
add a constitutional stage were the policy instruments are exogenous and you integrate
if and only if there is a plurality in both jurisdictions. In this overly simple framework,
it can be show that countries never integrate. The reason is that the poor majority in
the region which exports capital is always worse off. There are three effects: they lose
some control over the rich in their jurisdiction due to the fiscal competition; they have
less capital to work with so they get lower wages; and they gain in after–tax capital
13
income. But the latter and sole beneficial effect can be shown to never dominate.16
So the conclusion would be that autarky is chosen if it is good (Proposition 1), but
integration is not chosen even if it is good (Proposition 2). Yet, one should not place
too much emphasis on this conclusion because doing so would mean to over interpret
results from a model not designed or equipped for these questions. Constitutional negotiations are complicated political processes; they are not only about who you partner
with, they are also about endogenous constitutional restrictions on policy instruments
and on the nature of the system of governance itself (e.g. determination of equilibrium
voting system). The role of normative analysis, of course, is to make some attempt at
informing and influencing that complicated constitutional political process which leads
to the determination of equilibrium institutions.
Finally, we did not address explicitly the implications of centralization in our model.
Suppose in a fully integrated economy with a centralized redistributive function, a uniform tax rate is democratically chosen.17 Consequently, the capital allocation between
the two countries (regions) will be efficient under centralization. Also, because there is
no possibility of capital flight from the unified economy, there is no potential for a race
to the bottom with tax competition. Thus, the coordination advantages of centralized
decision making are captured to the extreme. But even with centralization, integration
may hurt the poorest individuals in the economy. The logic is simple. As has already
been noted by, e.g., Bolton and Roland (1997), centralization will generally change the
ruling majority. It may therefore entail a loss of political power for the poor in the
poorer country and thus may lead to less preferred outcomes from their perspective.
16
Without loss of generality assume country 1 is the exporter. Given ρ∗ ≥ 0 using (2), and due to
the capital outflow, k1∗ − k1m < 0 is necessary for the majority in the exporting country to be better
off with integration. It follows that k1∗ < k1m < k by our assumption kjm < k. Hence k1∗ < k < k2∗ from
(k1∗ + k2∗ )/2 = k, which implies k2m < k < k2∗ under our assumption again. Therefore, f 0 (k2∗ ) < f 0 (k1∗ )
or t∗1 > t∗2 by (4). But using (8) then yields t∗1 < 0 < t∗2 , a contradiction.
17
The assumption of a uniform federal policy is frequently imposed in the literature on fiscal federalism [see Oates (1972)]. Although it is certainly empirically relevant, it lacks motivation to a certain
extent as it may involve a welfare loss if regions should be treated differently from an efficiency perspective [see e.g., Besley and Coate (1999) and Lockwood (1998)]. While this problem is of no concern
in our model, a ruling majority in one country may still want to set distinct tax rates in order to
change the international factor allocation to its favor.
14
References
Bucovetsky, S. (1991), “Asymmetric Tax Competition,” Journal of Urban Economics,
30, 167-181.
Besley, T. and S. Coate (1999), “Centralized vs. Decentralized Provision of Local
Public Goods: A Political Economy Perspective, NBER working paper.
Bolton, P. and G. Roland (1997), The Break-Up of Nations: A Political Economy
Analysis, Quarterly Journal of Economics, 112, 1057-1090.
Edwards, J. and M. Keen (1996), “Tax Competition and Leviathan,” European Economic Review 40, 113-134.
European Commission (1998), Conclusions of the ECOFIN Council Meeting on 1
December 1997 concerning taxation policy, OJ 98/C2/01.
Grandmont, J.-M. (1978), Intermediate Preferences and the Majority Rule, Econometrica, 46, 317-330.
Hamada, K. (1966), “Strategic Aspects of Taxation on Foreign Investment Income”
Quarterly Journal of Economics, 80, 361–375.
Kessler, A., C. Lülfesmann and G. Myers (1998), “Redistribution, Fiscal Competition,
and the Politics of Economic Integration,” mimeo, University of Bonn.
Laussel, D. and M. Le Breton (1998), ”Existence of Nash Equilibria in Fiscal Competition Models”, Regional Science and Urban Economics, 28, 283-296.
Lockwood, B. (1998), “Distributive Politics and the Benefits of Decentralisation”,
mimeo, University of Warwick.
Oates, W. E. (1972), Fiscal Federalism, New York: Harcourt Brace Jovanovich.
Organisation for Economic Cooperation and Development (1998), Harmful Tax Competition: An Emerging Global Issue, Paris: OECD.
Perotti, R. (1993), “Political Equilibrium, Income Redistribution, and Growth,” Review of Economic Studies, 60, 755–776.
15
Persson, T. and G. Tabellini, (1992) “The Politics of 1992: Fiscal Competition and
European Integration,” Review of Economic Studies, 59, 689–701.
Sinn, H. W. (1994), “How Much Europe? Subsidiarity, Centralization, and Fiscal
Competition,” Scottish Journal of Political Economy, 41, 85-107
Wildasin, D. E. (1988), “Nash Equilibrium in Models of Fiscal Competition,” Journal
of Public Economics, 35, 229-40.
Wilson, J. D. (1987), “Trade, Capital Mobility, and Tax Competition,” Journal of
Political Economy, 95, 835–856.
Wilson, J. D. (1991), “Tax Competition with Interregional Differences in Factor Endowments,” Regional Science and Urban Economics, 21, 423-451.
Wilson, J. D. (1999), “Theories of Tax Competition,” National Tax Journal, forthcoming.
Zodrow, G. R. and P. Miezskowski (1986), “Pigou, Tiebout, Property Taxation, and
the Underprovision of Local Public Goods,” Journal of Urban Economics, 19,
356–370.
16
Appendix 1
Derivation of the Best-Response Functions.
We start with some preliminary observations. First, in any equilibrium the capital stock in
the economy, k̄1 + k̄2 = 2k̄ is fully utilized. To see why, suppose to the contrary that some
capital is not invested, i.e., [k1 + k2 ]/2 < k̄, implying ρ = 0. The equilibrium capital stock
kj (t1 , t2 ) is then uniquely determined by
rj (kj ) − tj = 0,
j ∈ {1, 2}
(9)
with ∂kj /∂tj < 0. Using the fact that ρ = 0 in (2) yields cij = f (kj ) for all individuals.
Since lowering tj unambiguously increases kj , the population in j would unanimously prefer
a lower tax rate in such a situation, a contradiction. Hence, tbr
j (th ) is always such that
[k1 (·) + k2 (·)]/2 = k̄.
Next, due to our assumption kjm ≤ k̄, all equilibria must involve t∗j ≥ 0. To see this,
1
1
observe first that if tbr
j ≤ th we must have kj ≥ k̄ ≥ kh from (4) and 2 k1 + 2 k2 = k̄ (all
br
capital is used). Now suppose tbr
j < 0 so that ρ > 0. In this case, tj is determined by the
m
first-order condition (8). But (8) allows for tbr
j < 0 only if kj < kj which together with
m
br
kj < k̄ implies kj < k̄, a contradiction if tj ≤ th . Consequently, tbr
j (th ) ≥ 0 whenever
br
tj ≤ th and the result follows.
The preceding arguments have established that we can without loss of generality confine
attention to best response functions tbr
j (th ) that lie in the non-negative orthant and are such
that the economy-wide capital stock is fully employed. We are now in a position to derive
those functions and their properties in more detail. In doing so, we follow and extend the line
of argument in Laussel and Le Breton (1998) who consider completely symmetric countries
with kjm ≡ 0.
As already mentioned in the text, two cases must be distinguished:
br
i) First, suppose tbr
j (th ) is such that ρ(tj (th ), th ) > 0 so that kj is determined according to
(4) and (5) and (6) apply. Using the last two equations and the fact that ∂kh /∂tj = −∂kj /∂tj ,
the derivative of the objective function in (7) can be expressed as
∂cm
∂kj
∂ρ
j
=−
(kj − kjm ) + tj
∂tj
∂tj
∂tj
¤ ∂kj
∂kh £ 00
=−
f (kh )(kj − kjm ) + tj =
Gj (t1 , t2 , kjm ),
∂tj
∂tj
(10)
where Gj (t1 , t2 , kjm ) ≡ f 00 (kh )(kj − kjm ) + tj . Observe that Gj (tj , th , kjm ) < 0 for tj close to
zero and Gj (tj , th , kjm ) > 0 for tj sufficiently large (recall that we can confine attention to
non-negative tax rates, i.e., (t1 , t2 ) ≥ 0). Hence, there must exist a value tbr
j (th ) ≥ 0 such
br
br
br
that Gj (tj , th , ·) = 0. As long as ρ(tj (th ), th ) > 0, tj (th ) is the best response function as it
satisfies the first-order condition (8) by definition of Gj . Since at any such point,
∂kj
∂Gj ¯¯
f 000 (kh ) ∂kj br
= 1 + f 00 (kh )
+ 00
t > 0,
¯
∂tj Gj =0
∂tj
f (kh ) ∂tj j
17
the best reply tbr
j (th ) not only exists, but is also unique. Furthermore, applying the implicit
function theorem, using ∂kh /∂th = ∂kj /∂tj , yields
∂k
000
∂k
(kh )
j br
f 00 (kh ) ∂tjj + ff 00 (k
t
dtbr
∂Gj /∂th
j
h ) ∂tj j
=−
=
∈ (0, 1).
000
∂k
(kh ) ∂kj br
dth
∂Gj /∂tj
1 + f 00 (kh ) ∂tjj + ff 00 (k
t
h ) ∂tj j
Hence, best responses are increasing with a slope less than unity. Finally, let us derive the
range of th for which case i) applies. To this end, note that
dρ
∂ρ
∂ρ dtbr
j
=
+
< 0,
dth
∂th ∂tj dth
so that there exists a unique value of t̃h such that ρ(tbr
j (t̃h ), t̃h ) = 0. For all values th ≤ t̃h ,
tbr
is
indeed
defined
by
(8)
and
the
constraint
ρ(·)
≥
0
is (weakly) not binding.
j
br
ii) Next, suppose th > t̃h so that tj as defined by (8) or Gj (·) = 0 would imply ρ(·) = 0
with the capital stock not fully utilized so that (5) and (6) no longer apply. From our
argument above, best replies will now ensure that all capital is used in equilibrium, i.e.,
kj (tbr
j ) + kh (th ) = 2k̄ must hold, with country j’s capital stock being determined by (9) as a
function of tj only. Totally differentiation using k1 (t1 ) + k2 (t2 ) = 2k̄ and (9) yields
dtbr
f 00 (kj )
j
= − 00
< 0 with
dth
f (kh )
dtbr
j
R −1 ⇔ tbr
j Q th .
dth
(11)
To summarize, for th ∈ [0, t̃h ], the best reply tbr
j of country j is a single valued, positive
and increasing function of th . The net return to capital decreases in th and becomes zero at
br
(tbr
j (t̃h ), t̃h ). From then on (for values th ≥ t̃h ), tj is a single valued, positive function which
is decreasing in th and we have ρ ≡ 0.
Existence, Properties, and Uniqueness of Equilibrium.
The equilibrium (t∗1 , t∗2 ) is where the two best reply functions intersect. We proceed by way of
a graphical argument. There are two possibilities to consider, which are illustrated in Figure
1 (a) and (b) respectively.
Suppose first the reaction functions cross at a point where ρ∗ > 0 so that case i) applies
[Figure 1 a)]. Since their slope is positive and less than unity, this intersection point is clearly
unique. Also, it will lie off the diagonal if the equilibrium is asymmetric (k1m 6= k2m ) and on
diagonal otherwise (k1m = k2m ).
Next, suppose case ii) is applicable and ρ∗ = 0 [Figure 1 b)]. Note that this requires
tbr
j (t̃h ) > t̃h for both countries so that the turning point of each reaction function emerges
above (respectively, below) the diagonal. This is the only remaining case because there can
be no intersection at a point where one curves slopes downwards while the other curve slopes
upwards (as this would mean ρ = 0 and ρ > 0 simultaneously hold).
As drawn, the reply functions are not symmetric and intersect at a point where t∗1 < t∗2
(the possibility where t∗1 > t∗2 is analogous). To see why multiple equilibria cannot emerge in
such a situation, reconsider (11). Starting from tbr
1 (t̃2 ) > t̃2 , country 1’s reply has a negative
slope, which is at first steeper than −1, then equal to −1 at tbr
1 (t2 ) = t2 and further flattens
18
t1 6
tbr
2
t1
6
tbr
2
t∗1 ...................................r
...
...
...
...
...
...
...
...
..
t∗2
Figure 1 (a)
t∗1 ...................r
...
....
tbr
...
1
...
...
...
...
...
- t
..
2
t∗2
Figure 1 (b)
tbr
1
-
t2
out for t1 > t2 . This property is a direct consequence of our assumption f 000 (·) ≥ 0 which not
only ensures equilibrium existence, but also implies that the negatively sloped segments of tbr
j
are weakly convex to the origin. Obviously, therefore, those segments can intersect at most
once provided that they are not mirror images of each other, i.e., some asymmetry is present.
Also, this intersection point must involve t∗1 6= t∗2 ⇔ k1∗ 6= k2∗ from (9) because otherwise, the
slopes would be identical [see (11)], which is clearly impossible.
For identical decisive majorities with k1m = k2m , however, t̃1 = t̃2 = t̃ and the two segments
coincide over the range [t̃, tbr (t̃)]. Hence, all combinations (t∗1 , t∗2 ) that lie on the joint arc of
both segments form an equilibrium [see also Laussel and Le Breton (1998)]. In particular,
this includes the (focal) point at the diagonal where t∗1 = t∗2 . For the proof of Proposition
2, finally note that for k1m = k2m < k̂, we have tbr (t̃) > t̃ by definition of t̃ and k̂. As argued
above, the reaction functions no longer intersect over the range where both are positively
sloped, so only points over the range [t̃, tbr (t̃)] that lie on the curve common to both negative
segments are equilibria.
Appendix 2
Here, we provide two examples that do not display the extreme property of expropriative taxation of capital in autarky. Recall that the abstraction which leads to expropriative taxation
is the assumption that taxation is not costly or distortionary. To alter this assumption in the
simplest way, we assume that there are no costs of capital taxation at low enough levels but
that once taxation reaches a critical level, t¯j = αrj (kj ) with 0 < α < 1, there are prohibitive
costs of further taxation.18
18
For the cost of raising taxes above t¯j to be prohibitive the marginal cost of increasing tj must be
greater than k¯j − kjm , which is the marginal benefit for the median voter. The assumption that total
costs are zero for tj ≤ t¯j is obviously strong. But our qualitative results also go through with positive
19
We assume a Cobb–Douglas production function or f (kj ) = bkja with 0 < a < 1. Given
this production technology and the cost of public funds as specified above, utility for individual i located in country j in political equilibrium under autarky is given by
i
ciA
j = f (kj ) − [rj (kj ) − tj ][kj − kj ]
a
= bkj − [1 − α]abkj
a−1
[kj − kji ].
To generate our numerical examples for integration we choose values for all parameters and
solve (4), (k1 + k2 )/2 = k̄, and (8) for the capital allocation and taxes. At this allocation and
tax levels, if ρ > 0 then by the results in Appendix 1 we have the unique political equilibrium
under integration {t∗1 , t∗2 , k1∗ , k2∗ } with ρ∗ = ab[k1∗ ]a−1 −t∗1 and the utility of individual i located
in country j in political equilibrium under integration is given by
∗ a
∗ ∗
i
ci∗
j = b[kj ] − ρ (kj − k )
To make the welfare comparisons we assume cardinal ratio scale comparability. We also use
the standard social choice axiom of anonymity. These assumptions lead to the following
welfare function,
X
−1
W = ( (ci )−v ) v for v ≥ −1andv 6= 0
i
=
Y
ci for v = 0
i
For this function the aversion to inequality is 0 at v = −1 (classical utilitarianism) and is
infinite as v → ∞ (Rawlsian).
Example Where Autarky Dominates.
We assume two classes of individuals i ∈ {P, R} with the poor in a 2/3-majority in each
country. We then assume values for all parameters as follows: a = 1/2, b = 1, k̄ = 1,
k¯1 = 21/20, k¯2 = 19/20, k1P = 1, k1R = 23/20, k2P = 0, k2R = 57/20, and α = 0.9. Thus
k1m = 1 and k2m = 0. For autarky t¯j = αrj (k¯j ) or t¯1 = 0.439 and t¯2 = 0.462. The solutions for
the equilibrium values under integration are k1∗ = 1. 185, k2∗ = 0.815, ρ∗ = 0.396, t∗1 = 0.063,
t∗2 = 0.158, r1∗ = 0.459, and r2∗ = 0.554.19 .
This leads to the following equilibrium allocation under autarky: cP1 A = 1.022, cRA
=
1
P ∗ = 1.015, cR∗ = 1.075, cP ∗ = 0.580,
1.030, cP2 A = 0.926, cRA
=
1.
072.
For
integration
it
is:
c
2
1
1
2
cR∗
2 = 1.709.
The difference between welfare with integration and welfare with autarky at v = −1 is
−0.024, at v = 0 it is −0.353, and as v → ∞ it is −0.346. The first is consistent with lower
output under integration due to capital flowing in the wrong direction (the capital rich region
imports capital) and the last is consistent with integration hurting the poorest in the economy
(the poor in the poor country). By plotting the difference, it is decreasing for −1 < v < 0,
it is discontinuous at v = 0, and it is decreasing for finite v > 0. Thus, in this example
total costs of taxation as long as the costs are too large.
19
Note t∗j < αrj∗ in all examples
20
where taxation is not expropriative and both countries and voters are asymmetric, autarky
dominates under any aversion to inequality.
Example Where Integration Dominates.
Again, let individuals (endowment classes) i = P, R be such that the poor are in a 2/3majority in each country. We then assume values for all parameters as follows: a = 1/2,
b = 1, k̄ = 1, k¯1 = 7/4, k¯2 = 1/4, k1P = 1, k1R = 13/4, k2P = 0, k2R = 3/4, and α = 0.9.
Thus again k1m = 1 and k2m = 0. For autarky t¯j = αrj (k¯j ) or t¯1 = 0.340 and t¯2 = 0.900.
The solutions for variables at equilibrium for integration are exactly those for the previous
example because the characteristics of the majority are unchanged: k1∗ = 1. 185, k2∗ = 0.815,
ρ∗ = 0.396, t∗1 = 0.063, t∗2 = 0.158, r1∗ = 0.459, and r2∗ = 0.554.
This leads to the following equilibrium allocation under autarky: cP1 A = 1.295, cRA
=
1
P
A
RA
P
∗
R∗
P
∗
1.380, c2 = 0.475, c2 = 0.550. For integration it is c1 = 1.015, c1 = 1.907, c2 = 0.580,
cR∗
2 = 0.877.
The difference between welfare with integration and welfare with autarky at v = −1 is
0.505, at v = 0 it is 0.293, and as v → ∞ it is 0.105. The first is consistent with higher output
under integration due to capital flowing in the right direction and the last is consistent with
integration helping the poorest in the economy. By plotting the difference, it is increasing for
−1 < v < 0, it is discontinuous at v = 0, and increasing for finite v > 0. Thus, in this example
where taxation is not expropriative (ρ∗ > 0) and both countries and voters are asymmetric,
integration dominates under any aversion to inequality.
21